Stimulating Discussion Around “What We Know” About Strengthening

High School Mathematics Programs and Outcomes

National High School Center’s Summer Institute

Breakout 5Thursday, June 19, 2008

Steven J. Leinwand

Principal Research Analyst, American Institutes for Research

Scary Perspective 1

As mathematics colonizes diverse fields, it develops dialects that diverge from the “King’s English” of functions, equations, definitions and theorems. These newly important dialects employ the language of search strategies, data structures, confidence intervals and decision trees.

- Steen

Scary Perspective 2

Evidence from a half-century of reform efforts shows that the mainstream tradition of focusing school mathematics on preparation for a calculus-based post-secondary curriculum is not capable of achieving urgent national goals and that no amount of tinkering is likely to change that in any substantial degree. - Steen

If Not Tinkering, Then Thinking Systemically:

A guiding vision of teaching and learning Adjust the curriculum – less IS more Focus on instruction Students need to grapple/struggle a little Focus on big ideas/conceptual understanding Ensure professional sharing and collegial

interaction High quality, common and aligned

assessments

Based on what?

or

What we know or sorta know.

From: Report on Key Practices and Policies of Consistently Higher Performing High Schools

Higher performing high schools tend to: set explicit academic goals – aligned with and often

exceeding state standards; support a culture of collaboration with focused

professional development activities; and provide teachers with the tools that will help them

meet those goals – for all students – and focus on broader learning objectives than just their own subject matter.

More Specifically: Extended class periods; Special catch-up courses; 9th grade academies; High-quality and well-defined curricula; In-service training on these curricula; Efforts to create professional learning

communities; Provide relevant data and accessible data systems; Provide targeted interventions to meet the needs of

struggling students; and Provide recognition of both teachers and students.

From Emerging Evidence on Improving High School Student Achievement and Graduation Rates

The larger lesson of this synthesis is that structural changes to promote personalization and instructional improvement are the twin pillars of high school reform.

Small learning communities and faculty advisory systems can increase students’ feelings of connectedness to their teachers.

From SREB: High Schools That Work

Key Practices: High expectations – setting and achieving

them Career/technical studies – applying the

math and science Academic studies – increasing access to

the college prep curriculum Work-based learning Teacher collaboration

SREB (continued):

Key Practices (continued): Actively engaged students; Guidance – so students don’t take the

easy way out; Extra help and time; and Keeping score for continuous

improvement and accountability.

And then there is Jo Boaler’s work:

Action Typical HS Railside HS

Lecture 21% 4%

Questioning 15% 9%

Individual Work Practicing

48%

Group Work 72%

Student Presentation 0.2% 9%

Typical High School Class: 2.5 minutes/problem 24 problems/class

Railside High School Class: 5.7 minutes/problem 16 problems/90 minute period

Jo Boaler’s Work: Multidimensional Classes

“In many classrooms there is one practice that is valued above all others – that of executing procedures (correctly and quickly). The narrowness by which success is judged means that some students rise to the top of classes, gaining good grades and teacher praise, while others sink to the bottom with most students knowing where they are in the hierarchy created. Such classrooms are unidimensional.”

Jo Boaler’s Work: Multidimensional Classes

“At Railside the teachers created multidimensional classes by valuing many dimensions of mathematical work. This was achieved, in part, by having more open problems that students could solve in different ways. The teachers valued different methods and solution paths and this enabled more students to contribute ideas and feel valued.”

When there are many ways to be successful, many more students are successful.

“When we interviewed the students and asked them “what does it take to be successful in mathematics class?” they offered many different practices such as: asking good questions, rephrasing problems, explaining well, being logical, justifying work, considering answers…

When we asked students in “traditional” classes what they needed to do in order to be successful they talked in much more narrow ways, usually saying that they needed to concentrate, and pay careful attention.”

Jo Boaler’s Work

Other characteristics at Railside: Teaching students to be responsible for

each other’s learning; High cognitive demand; Effort over ability; and Clear expectations and learning practices

In other words: instruction matters!

So, To Recapitulate, Thinking Systemically:

A guiding vision of teaching and learning Adjust the curriculum – less IS more Focus on instruction Students need to grapple/struggle a little Focus on big ideas/conceptual understanding Ensure professional sharing and collegial

interaction High quality, common and aligned

assessments

Resources

National High School Center

www.betterhighschools.org Report on Key Practices and Policies of

Consistently Higher Performing High Schools Emerging Evidence on Improving High

School Student Achievement and Graduation Rates: The Effects of Four Popular Improvement Programs

Resources

Southern Regional Education Boardwww.sreb.org

High Schools that Work project Partnership for 21st Century Skills

www.21stcenturyskills.org Results that Matter

Achieve, Inc. www.achieve.org

American Diploma Project

Resources

Jo Boaler’s Research http://www.stanford.edu/~joboaler/equitable.pdf

Horizon ResearchTitle: Status of High School Mathematics Teachinghttp://2000survey.horizon-research.com/reports/

high_math/high_math.pdf

Questions?

Comments?

Initial Reactions?